For bifibrations in small categories, the length of cup products in the kernel of an induced Baues-Wirsching cohomology map lower-bounds the Svarc genus.
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Computes LS-category and bounds on topological complexity for real torus manifolds and Dold manifolds of real torus type, showing TC equals 2n or 2n+1 under hypotheses and exact symmetric TC values in infinitely many cases.
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Baues-Wirsching Cohomology and Svarc Genus in Small Categories
For bifibrations in small categories, the length of cup products in the kernel of an induced Baues-Wirsching cohomology map lower-bounds the Svarc genus.
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LS-category and topological complexity of real torus manifolds and Dold manifolds of real torus type
Computes LS-category and bounds on topological complexity for real torus manifolds and Dold manifolds of real torus type, showing TC equals 2n or 2n+1 under hypotheses and exact symmetric TC values in infinitely many cases.